ArticlePDF Available

Structural and architectural evaluation of Chinese rainbow bridge and related bridge types using BESO method

Authors:

Abstract and Figures

Abstract With timber pieces to weave a large span, the Chinese rainbow bridge in the famous painting entitled “Scenery along the River During the Qingming Festival” shows a special structural type. According to its arch shape, joints and construction technology, the rainbow bridge is perhaps an optimized design in its historical context. This hypothesis motivates us to use topology optimization methods to evaluate the timber woven-arch system. This paper firstly overviews present studies on structural performance of the Chinese rainbow bridge and the bi-directional evolutionary structural optimization (BESO) method. Next, this study evaluates the rainbow bridge’s structural and architectural features using BESO. Then, this paper evaluates extant timber lounge bridges related to the Chinese rainbow bridge using the BESO method to reveal advantages and disadvantages. By matching woven patterns of the traditional Chinese rainbow bridge and force-flow patterns generated by BESO, a novel evaluation method for complex forms is introduced. Keywords: Chinese rainbow bridge, BESO, Structural optimization, Woven-arch, Ameba software (15) (PDF) Structural and architectural evaluation of Chinese rainbow bridge and related bridge types using BESO method. Available from: https://www.researchgate.net/publication/348740810_Structural_and_architectural_evaluation_of_Chinese_rainbow_bridge_and_related_bridge_types_using_BESO_method [accessed Jan 25 2021].
Analyzing design region as a curved beam 4.2. Analyzing the three-segment arch system and the four-segment arch system The following evaluation assumes the Bianhe rainbow bridge as the arch type with vertical and horizontal supporting. Here, symmetric loads are applied for analyzing. Based on joint types, there are two options to analyze polygonal arch systems, without or with considering the effect of joints as no design region. The first two rows of Figure 7 show force-flow patterns of the three-segment arch analyzed by BESO. Results of two options are almost the same. Shoulders of the arc design region were removed firstly because of low-stressed material, then the middle top part was removed gradually, so that the three-segment arch system was calculated. But during the evolving procedure, a beam-like part near the load area was evolved. It is true that the final geometry would be shaped as the polygonal arch which is the best optimization, but for designers any result in each iteration step could be a design option. The last two rows of Figure 7 show force-flow patterns of the four-segment arch evolved by BESO. Results are similar whatever considering constraints of joints or not. During the early calculation stage, shoulder areas between concentrated loads were removed quickly. Then the middle part in the span started to be removed with the trend to be four-segment polygonal arch. But interesting thing is results show a beam-like area near the top load. One solution for design could be arch-beam mixed system. Comparing the force-flow pattern with the geometry pattern, peak A and E areas match
… 
Content may be subject to copyright.
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
July 16-20, 2018, MIT, Boston, USA
Caitlin Mueller, Sigrid Adriaenssens (eds.)
Copyright © 2018 by < Xianchuan Meng, Qiang Zhou, Wei Shen, Yi Min Xie>
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Structural and architectural evaluation of Chinese rainbow bridge
and related bridge types using BESO method
Xianchuan Meng a, *, Qiang Zhou b, Wei Shen b, Yi Min Xie b, c, *
a School of Architecture and Urban Planning, Nanjing University, Nanjing 210093, China
mxc@nju.edu.cn
b XIE Archi-Structure Design (Shanghai) Co., Ltd., Shanghai 200092, China
c Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne 3001, Australia
mike.xie@rmit.edu.au
Abstract
With timber pieces to weave a large span, the Chinese rainbow bridge in the famous painting entitled
Scenery along the River During the Qingming Festival shows a special structural type. According to
its arch shape, joints and construction technology, the rainbow bridge is perhaps an optimized design
in its historical context. This hypothesis motivates us to use topology optimization methods to evaluate
the timber woven-arch system. This paper firstly overviews present studies on structural performance
of the Chinese rainbow bridge and the bi-directional evolutionary structural optimization (BESO)
method. Next, this study evaluates the rainbow bridges structural and architectural features using
BESO. Then, this paper evaluates extant timber lounge bridges related to the Chinese rainbow bridge
using the BESO method to reveal advantages and disadvantages. By matching woven patterns of the
traditional Chinese rainbow bridge and force-flow patterns generated by BESO, a novel evaluation
method for complex forms is introduced.
Keywords: Chinese rainbow bridge, BESO, Structural optimization, Woven-arch, Ameba software
1. Introduction
In China, a special type of timber arch bridges was invented using straight logs as polygonal arches to
achieve a large span around the 11th century which is called Bianhe rainbow bridge in the famous
painting entitled Scenery along the River During the Qingming Festival (Figure 1-1) [1]. The
invention time of the rainbow bridge is earlier than that of timber trusses [2]. The rainbow bridges
related structural types with timber lounge still exist in Chinese southern area (Figure 1-2) [3]. It is
supposed that the original design of rainbow bridge was inspired by the Chinese old folk game on
using chopsticks to build a toy bridge (Figure 1-3). To preserve this unique handicraft art, the
traditional construction technology is on the list of the Intangible Cultural Heritage of UNESCO since
2009. The similar design was invented by Leonardo de Vinci for the military usage (Figure 1-4) [4].
According to its shape, joints and construction technology, the rainbow bridge is perhaps an optimized
design in its historical context. This hypothesis motivates us to use topology optimization methods to
evaluate the timber woven-arch system.
Figure 1: Bianhe rainbow bridge, extant woven-arch bridge, a folk game [1] and Leonardo de Vincis bridge [4]
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
2
2. Brief review of the timber woven-arch bridge
The original painting was drawn by a realist painter Zeduan Zhang in the Song dynasty. According to
sizes of buildings and humans, the bridge was analyzed as spanning 18.5m with 9m width and 4.5m
raise [2] as shown in Figure 2. The framework of this bridge consists of two styles of arch systems,
one is three-segment arch system and the other is four-segment arch system. The three-segment arch
system with ten parallel members is connected by two transverse beams. The four-segment arch
system with eleven parallel members is connected by three transverse beams. For each system,
transverse beams serve as joints in the polygonal arch ribs.
Figure 2: The sketch of Bianhe rainbow bridge, on the left, and its analyzed size, on the right
The existing Chinese timber woven-arch bridge in southern China has a lounge along the bridge.
Because they are located in two provinces called Min and Zhe, these bridges are called Min-Zhe
timber arch bridges [3]. Bianhe rainbow bridge and Min-Zhe timber arch bridges are related. The
number of existing Min-Zhe timber arch bridge is more than 100 [5], and more bridges are planned to
be built. But there are only several existing rainbow bridges. Jinze rainbow bridge in Shanghai is one
example, which was designed by Huancheng Tang, a specialist of bridges in China, and Bashar
Altabba, a structural engineer in MIT. The project was supported by the WGBH Nova, an American
TV program (Figure 3) [2]. During the construction process, there was a debate on the structural
performance of woven arches. Some scholars argued that the woven-arch acted as arches while others
considered it as a beam-arch structure. Recent structural analyses of Chinese traditional timber arch
bridges focus on performance and offer interesting suggestions [6,7]. Unfortunately, they can hardly
provide a global view to understand the behavior of woven arches.
Figure 3: Jinze rainbow bridge in Shanghai and one moment during its construction process (photos by J. Liu)
3. Brief review of bi-directional evolutionary structural optimization (BESO)
Finite element analysis approaches are more and more powerful especially with the advances of digital
technologies. Most of them work as the post analytical tools based on the predetermined conceptual
geometries offered by form designers. The analyzing process usually is static which is good for
designers who want to know whether the form is structurally safe and which structural areas should be
strengthen. But for who attempts to achieve efficient structures, static finite elementary analysis
approach would be a passive strategy.
Addressing geometrical topology changes structural optimization approach deals with archiving best
optimized structural performance of a predetermined form including the topology, contour and
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
3
elementary sizes. As the practical finite elementary method, several general topology optimization
approaches have been established and applied to many projects in different areas during past three
decades, including aerospace industry, civil engineering and architecture design [8] [9] [10] [11].
Among them, the evolutionary structural optimization (ESO) approach developed as a popular method
especially within structural engineers and architects due to its simplicity of implementation [12]. Bi-
directional evolutionary structural optimization (BESO) as its developed approach becomes more
powerful. BESO could not only remove the inefficient material from the original structure, but also
add material to the most demanding areas simultaneously [13] [14].
4. Evaluation of the rainbow bridge using BESO approach
Previous studies on the arch system of rainbow bridge usually simplify the log arch system as line
schemes and analyze their bending moments and axis forces (Figure 4). It is good for designers to
prove straight logs structurally safe, but lack of evaluation of the whole structure in a global
perspective.
Figure 4: Analyzing arch systems with simplified line-schemes
With the consistence of removing redundant material and adding demanding material at each iteration
with the von Mises stress criterion and strain energy density criterion, the robust BESO approach
would evolve a structure from an initial geometry with very crude shape into a completely different
shape with better structural performance [15]. One kind of design strategy is to apply the modified
result by BESO as the final design [8]. In this paper authors attempts to use BESO in a novel way to
balance the design of the desired geometry and the design of the efficient structure.
The desired geometry for designers would be very specific but could be abstracted into a rough
boundary, which is called geometry pattern. The efficient structure could be the final optimized
result by BESO, but also could be any optimization during the procedure of iterations, because all of
them are more structurally efficient than the initial geometry. The less remaining area keeps, the more
structural efficiency performs. Those optimizations illustrate the diversity of forces flows and load
path inside the initial geometry called force-flow pattern. The rough geometry is a design region,
the domain to be optimized by BESO. Inside the design region there is some area as geometry
restraints called non-design area, which attracts initial forces to path by and would strongly influent
the outcome of force-flow patterns.
The design pattern could produce the crude design region and specific non-design area. With
other appropriate boundary conditions, such as restraints and loads, the force-flow pattern would be
evolved by BESO. The comparative study between design pattern and force-flow pattern could
inspire designer to make design strategies including to refine geometry or select possible boundary
conditions. The diversity of force-flow pattern encourages the possibilities of design strategies.
Ameba is a developed software of BESO running on the parametric platform. This paper applies
Ameba as an aided analysis tool.
Figure 5 shows a study model to evaluate Bianhe rainbow bridge. Woven is the character of geometry
pattern for Bianhe rainbow bridge. The woven outline of rainbow bridge could be described as peaks
and valleys, and there are five peaks, A, B, C, D and E, and four valleys. Considering the thickness of
two arch systems including joints, the design region could be treated as an arc layer with one-meter
thickness. In practice it is easier to find logs with diameter less than 30 centimeters, and the thickness
of three layers of logs would be about 1 meter. Based on the investigation of existing timber woven-
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
4
arch bridges and the historical records on joints, at least four types of joints are applied in practice.
Type a is a banding joint with hemp ropes, type b is a joint with Chinese long iron nails, type c and d
are joints with tenon and mortise connections. Type a, b and c tie two arch systems together and make
the interwoven system behave in a complicated way which is the reason to apply non-design area.
Type d keeps two arch systems away and unnecessary to use non-design area.
Figure 5: One-meter thickness design region, on the left, and several kinds of joints in arch systems, on the right
(photos a and b [1], c and d by Y. Liu)
4.1. Analyzing design region as a curved beam
Sometimes the woven-arch bridge would be thought as a curved beam. The support condition of the
design region could be set as the simple beam supporting, and with five concentrated loads. Through
the calculating process of BESO, the area near the axis layer was removed step by step which means
the removed part is with low stress and structural inefficient. As a result, a curved hollow desk was
shaped (Figure 6). The smooth upper and lower surfaces of this deck are different from the woven
geometrical pattern. Without the lateral supporting, internal forces of compression and tension would
be separated to opposite directions as a truss to resist the bending moment along the curved beam.
Figure 6: Analyzing design region as a curved beam
4.2. Analyzing the three-segment arch system and the four-segment arch system
The following evaluation assumes the Bianhe rainbow bridge as the arch type with vertical and
horizontal supporting. Here, symmetric loads are applied for analyzing. Based on joint types, there are
two options to analyze polygonal arch systems, without or with considering the effect of joints as no
design region. The first two rows of Figure 7 show force-flow patterns of the three-segment arch
analyzed by BESO. Results of two options are almost the same. Shoulders of the arc design region
were removed firstly because of low-stressed material, then the middle top part was removed gradually,
so that the three-segment arch system was calculated. But during the evolving procedure, a beam-like
part near the load area was evolved. It is true that the final geometry would be shaped as the polygonal
arch which is the best optimization, but for designers any result in each iteration step could be a design
option. The last two rows of Figure 7 show force-flow patterns of the four-segment arch evolved by
BESO. Results are similar whatever considering constraints of joints or not. During the early
calculation stage, shoulder areas between concentrated loads were removed quickly. Then the middle
part in the span started to be removed with the trend to be four-segment polygonal arch. But interesting
thing is results show a beam-like area near the top load. One solution for design could be arch-beam
mixed system. Comparing the force-flow pattern with the geometry pattern, peak A and E areas match
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
5
well. But peak C area shows mismatching. Taking the historical context into account, the three-
segment arch system is easy to be stable with symmetric loads, but it is very hard to get structurally
right four-segment arch geometry especially when craftsmen designed bridges only with experience
but without the structural design theory.
Figure 7: Analyzing the three-segment arch system and the four-segment arch system with BESO
4.3. Evaluating the woven-arch system
When analyzing the three-segment arch system and the four-segment arch system respectively, there
are almost no difference between considering joints or not. But the differences appear once two
systems interweave together. The reason to evaluate two systems in a plan is that two polygonal arch
systems attach each other in the real woven-arch structure. Figure 8 shows analyzed results with
symmetric concentrated loads. As shown in the first row of Figure 8, when ignoring the connecting of
two arch systems, the early removed part was in the middle part, then the shoulder parts became truss-
like shapes, and at the end the remained branches looked like a three-hinged arch with beams on
shoulders. As show in the second row, when applying the non-design area on the top, the force flow in
the middle span would transfer on the top part. As shown in the third row, when considering five-joint
connections as non-design areas, lower parts under shoulders were removed firstly, then the middle
part, which produced a beam-like arch. With the help of joints fix two arch systems together, the force
flow transferred as a three-segment arch.
Figure 8: Symmetrical loading case analyses of woven arches
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
6
The reason to discuss the combinations of design region and non-design area is that there are several
extant bridges are on the situation that some transverse beams cannot connect both arch systems. The
three combinations of design region and non-design area could represent three types of joint conditions.
As shown in Figure 8, type A is the woven-arch bridge with two separated arch systems which is
caused by foundations getting closer after built. Its force-flow pattern almost matches woven pattern.
Type B is the bridge with only one special transverse beam on the top connecting two arch systems.
The result shows that its force-flow pattern partly matches geometry pattern but not well in the area
between peak B and peak D. Type C is the bridge that all transverse beams attach two arch systems to
each other, which usually are assembled with long iron nails. The result shows that the force-flow
pattern almost matches the lower part of geometry pattern. Jinzhe rainbow bridge was built with type
C. Generally, three types have the potential to make force-flow pattern match geometry pattern well.
Asymmetrical load would strongly affect the structural behave of the woven arches. For instance,
loads on peak A, B and C are twice larger than loads on peak D and E (Figure 9). The results of force-
flow patterns do not match geometry pattern well, and the area between peak A and C cannot keep
weaving outlines. These results would suggest designers to avoid such loading condition when using
the woven geometry. Type A and B are similar in force-flow patterns, but different from type C where
the load path near peak D and E would act as a truss.
Figure 9: Asymmetrical loading case analyses of woven arches
4.4. Analyzing the woven system in 3D approach using BESO based tool Ameba
Ameba as the parametric BESO tool could offer the three-dimensional analyzing approach. Here are
two connected woven arches, one piece of the three-segment arch and one piece of the four-segment
arch. The initial design region is a pair of crude arc forms. Applying vertical and lateral supports,
setting five joints as non-design areas, but with different loading cases, the initial arc geometry evloves
into different force-flow patterns (Figure 10). When five equivalent forces are applied, the force-flow
pattern is alomst the woven-arch pattern of Bianhe rainbow bridge, but thicknesses of joints are quite
different. To achieve similar thickness of joints, the combination of concentrated forces is Q, 0.9Q,
0.8Q, 0.9Q, Q (loading case c in Figure 10).
Figure 10: 3D analysis of woven arches using BESO based tool Ameba
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
7
To prove that the force-flow pattern is a well optimized structure, we use the designed woven arches as
the structure (Figure 2) applying different loading cases to analyze. Figure 11 shows that with the
loading case parameters Q, 0.9Q, 0.8Q, 0.9Q, Q, the bending moments inside the structure are quite
small. But if applying loading cases of equivalent forces or decreasing three forces in the middle span,
the bending moments increase. The rigidly connection of joints (Figure 5) could help the whole woven
arches resist the bending moments. These analyses prove that the force-flow patterns generated by
BESO not only serve as efficient structures but also inspire design thinking on manipulate geometry
patterns.
Figure 11: Bending moment diagrams of woven arches with different loading cases
5. Evaluation of Min-Zhe timber lounge bridge with BESO
One important distinction between Bianhe rainbow bridge and Min-Zhe timber lounge bridge is that
Min-Zhe bridge could be considered as a rainbow bridge with timber corridors along the bridge
(Figure 1-2). One reason of the covered roof is to avoid getting wet from the local rainy weather.
Another reason could be derived from the comparation between the symmetric loading case on the
rainbow bridge (Figure 8) and the asymmetric loading case (Figure 9). The weight of the timber
lounge would help the loading situation close to the symmetric loading case which could conduct a
better structurally performance than rainbow bridge.
The timber lounge provides the woven-arch structure different boundary conditions, two more
supports on two upper ends and different loading conditions. The loading conditions would offer some
explanation about the difference of woven-arch systems between Bianhe rainbow bridge and Min-Zhe
timber lounge bridge. As shown in Figure 12, the distributed loads produced a branch-like pattern, but
the concentrated loads transferred from timber columns of the lounge could easily be located on the
peaks of woven arches. Furthermore, single external force in the middle would behave not as good as
two external forces in the middle span. The latter has more direct force flows to transfer load to
woven-arch systems. This would provide a structural reason why Min-Zhe bridges usually use the
three-segment arch system and the five-segment arch system to weave the structure.
Figure 12: analyzing Min-Zhe timber lounge bridges with BESO
6. Conclusion
Bianhe rainbow bridge is a complicated woven-arch system different from arches, beams and trusses.
With the operation on abstracting a geometry pattern into a design region, setting non-design areas
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
8
according to special requirements, and applying appropriate boundary conditions, the structurally
efficient force-flow patterns would be revealed by the BESO method. Through comparing the
geometry pattern with the force-flow pattern, design strategies would be inspired. In this case, by
matching woven geometrical pattern and the force-flow pattern produced by Ameba software,
advantages and disadvantages of the rainbow bridge in the historical context are illustrated, such as
supporting types, joint types and load conditions. In the future, the matching method between
geometry patterns and force-flow patterns with the BESO approach would be not only applied to
explain the structural behavior of existing complicated structures, but also used to design complex
fabricated forms inspired by the analysis of Chinese traditional timber woven-arch structures.
References
[1] H. Tang, Chinese Timber Arch-Bridges, China Architecture & Building Press, 2010 (in Chinese).
[2] B. Addis, Building: 3000 Years of Design, Engineering and Construction, Phaidon Press Limited,
2007.
[3] Y. Yang, S. Nakamura, B. Chen, and T. Nishikawa, "The Origin of Timber Arch Bridges in
China," Journal of Japan Society of Civil Engineers, vol. 2, no. 1, pp. 54-61, 2014.
[4] U. Thoennissen, Reciprocal Frameworks: Tradition and Innovation, gta Verlag, 2015.
[5] Y. Yang, S. Nakamura, B. Chen, and T. Nishikawa, Traditional construction technology of
China timber arch bridges, Journal of Structural Engineering, vol. 58A, pp. 777-784, 2012.
[6] Y. Liu, Typological study on timber arch bridges in Zhe-Min provinces:with focus on bridge-
deck-beam-system, Journal of Southeast University, vol. 2, pp. 430-436, 2011 (in Chinese).
[7] J. Sobieszczanski-Sobieski, RT. Haftka, Multidisciplinary Aerospace Design Optimization:
Survey of Recent Developments, Structural Optimization, vol.14, pp. 1-23, 1997.
[8] X.M. Xie, Z.H. Zuo, X. Huang, T. Black and P. Felicetti, Application of Topological
Optimisation Technology to Bridge Design, Structural Engineering International, vol. 24, pp.
185-191, 2014.
[9] M. Sasaki, Flux Structure, Toto, 2005.
[10] J. Burry, P. Felicetti, J. Tang, M. Burry and M. Xie, Dynamical Structural Modelling: a
Collaborative Design Exploration, International Journal of Architectural Computing, vol. 3, pp.
27-42, 2005
[11] Y.M. Xie, G.P. Steven, A Simple Evolutionary Procedure for Structural Optimization,
Computational Structure, vol. 49, pp. 885886, 1993.
[12] X. Huang, Y.M. Xie, M.C. Burry, A New Algorithm for Bi-directional Evolutionary Structural
Optimization, International Journal of the Japan Society of Mechanical Engineers, vol. C 49, pp.
1091-1099, 2004.
[13] X. Huang, Y.M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and
Applications, Wiley, 2010.
[14] Q. Chun, K.V. Balen, J. Pan and L. Sun, Structural Performance and Repair Methodology of the
Wenxing Lounge Bridge in China, International Journal of Architectural Heritage, vol. 9, pp.
730743, 2015.
[15] X. Huang, Y.M. Xie, Convergent and Meshindependent Solutions for the Bi-directional
Evolutionary Structural Optimization Method, Finite Elements in Analysis and Design, vol. 43,
pp. 1039-1049, 2007.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
Many timber lounge bridges are found in the south of Zhejiang Province and the north of Fujian Province in China. The timber lounge bridge is a unique type of timber arch bridge structure worldwide. Most of these bridges have some damages due to the influence by environmental impact and human action. In order to scientifically preserve these timber lounge bridges, their architectural configuration, structural performance, and damage mechanisms should be studied first, and then some adaptive repair methods can be put forward. The Wenxing Lounge Bridge is a famous and typical example of this type of bridge. This study investigated in detail how to repair the Wenxing Lounge Bridge. Since this bridge had much serious damage, such as asymmetric deformation, inclination and torsion, cracking and deflection of some timber members, and the slipping-off of the scissors braces and the crossbeams, and since the bridge occasionally swayed when people walked across it, it needed to be repaired urgently. Through the detailed on-site surveying and visits to the local bridge craftsmen, the architectural configurations and the damage characteristics of this bridge were understood. The finite element model analysis of this bridge before damage and after damage was made respectively to study the structural performance. Finally, the reasons for the damages of this bridge were analyzed and the adaptive repair design of the bridge is presented here. This work serves as a model for similar timber arch bridges.
Article
Full-text available
The increasing complexity of engineering systems has sparked rising interest in multidisciplinary optimization (MDO). This paper surveys recent publications in the field of aerospace, in which the interest in MDO has been particularly intense. The primary c hallenges in MDO are computational expense and organizational complexity. Accordingly, this survey focuses on various methods used by different researchers to address these challenges. The survey is organized by a breakdown of MDO into its conceptual components, reflected in sections on mathematical modelling, approximation concepts, optimization procedures, system sensitivity, and human interface. Because the authors' primary area of expertise is in the structures discipline, the majority of the references focus on the interaction of this discipline with others. In particular, two sections at the end of this review focus on two interactions that have recently been pursued with vigour: the simultaneous optimization of structures and aerodynamics and the simultaneous optimization of structures with active control.
Article
Full-text available
This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.
Book
From Egypt and Classical Greece and Rome through the building booms of the Gothic era and the Renaissance, and from the Industrial Revolution to the present era of digital modelling, Building: 3,000 Years of Design, Engineering, and Construction, charts centuries of innovations in engineering and building construction. This comprehensive and heavily illustrated volume, aimed at students and young professionals as well as general readers, explores the materials, classic texts, instruments, and theories that have propelled modern engineering, and the famous and not-so-famous buildings designed through the ages, from the Parthenon to Chartes Cathedral and the dome of St. Peter's, from eighteenth-century silk mills in England to the Crystal Palace, and on to the first Chicago high-rises, the Sydney Opera House, and the latest "green" skyscrapers. The book concentrates on developments since the industrial and scientific revolutions of the seventeenth and eighteenth centuries. Incorporated within the continuous narrative are sidebars with short biographies of eminent engineers, excerpts from classic texts, stories of individual projects of major importance, and brief histories of key concepts such as calculus. Also included are extensive reference materials: appendices, a glossary, bibliography, and index. Please note this book is for sale, e.g. via Amazon. It is not available via the author.
Article
The timber arch bridge in Zhejiang (Zhe) and Fujian (Min) provinces is a unique beam-weaving-arch structure, and has a close genetic relationship with the Rainbow Bridge in the famous Song-dynasty painting "the scene of the upriver at pure brightness festival". By a study of typological analysis focusing on the timber structure, it is pointed out in this paper that there is an important distinction between the timber arch bridge in Zhe-Min provinces and the Rainbow Bridge over the Bian River. Throughout the development of the former, the bridge-deck-beam-system has hold a significant role, and should be seen as the third system aside from the first and second systems, viz. the tri-segment arch, and the penta-segment arch. The signification in the bridge-deck-beam-system of timber arch bridge in Zhe-Min provinces includes: functionally, it provides a gentle-sloped floor for the bridge-deck; structurally, it shares the load of the arch, and serves the structural stability; typologically, the method of the combination of the bridge-deck-beam-system and the arch system provides an important factor of depicting the development of the typology of timber bridges. And an essential character of the evolvement of the structure of timber bridges is structure addition and simplification. The simplification and stabilization are the main motivation in the evolvement of timber arch bridges.
Article
This paper presents the application of modern topology optimisation technology to bridge design. Topology optimisation aims to determine the best locations and shapes of cavities in the design domain and therefore is capable of effectively dealing with structural design of infrastructure such as bridges. Several methods of topology optimisation have been developed during the past three decades, among which the evolutionary structural optimisation (ESO) method is popular because of its simplicity in software implementation and effectiveness in solving a wide range of engineering problems. The development of ESO and its advanced version bi-directional evolutionary structural optimisation (BESO) has reached a level of maturity nowadays. Applications of this technique have emerged around the world especially in the past decade. In this paper, the implementation of this technique in structural design is presented, with a particular focus on the design of various bridges. The design applications involve the consideration of different constructional requirements such as support types and selections of the elevation/span. Geometric constraints are also taken into account in the design problem, such as the periodic constraint with which a variety of architecturally aesthetic yet structurally efficient designs are produced. This paper aims to present the application of this promising technology to bridge design and to reveal its potential in a wider range of applications.
Article
In this paper, a new algorithm for bi-directional evolutionary structural optimization (BESO) is proposed. In the new BESO method, the adding and removing of material is controlled by a single parameter, i.e. the removal ratio of volume (or weight). The convergence of the iteration is determined by a performance index of the structure. It is found that the new BESO algorithm has many advantages over existing ESO and BESO methods in terms of efficiency and robustness. Several 2D and 3D examples of stiffness optimization problems are presented and discussed.
Article
A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.
Article
This paper will report on a generative performative modeling approach that engages architects and structural engineers in close dialog. We focus on knowledge shared between architects and engineers to apply the Finite Element Analysis based structural design technique Evolutionary Structural Optimization [ESO] as a way to understand or corroborate the performance factors that are significant in determining architectural form. ESO is very close conceptually to the dynamical system of matter and forces of growth itself. It has parallels both mathematical and metaphorical with natural evolution and morphogenesis so it has been poignant to apply the approach to a formal architectural case study in which the generative influence of these processes is inherent.